Singularities for a fully non-linear elliptic equation in conformal geometry
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Cita com:
hdl:2117/20686
Tipus de documentReport de recerca
Data publicació2013-08
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
We construct some radially symmetric solutions of the constant
k
-equation on
R
n
n
R
p
, which blow
up exactly at the submanifold
R
p
R
n
. These are the basic models to the problem of nding
complete metrics of constant
k
{curvature on a general subdomain of the sphere
S
n
n
p
that blow up
exactly at the singular set
p
and that are conformal to the canonical metric. More precisely, we look
at the case
k
= 2 and 0
<p<
p
2
:=
n
p
n
2
2
. The main result is the understanding of the precise
asymptotics of our solutions near the singularity and their decay away from the singularity. The rst
aspect will insure the completeness of the metric about the singular locus, whereas the second aspect
will guarantee that the model solutions can be locally transplanted to the original metric on
S
n
, and
hence they can be used to deal with the general problem on
S
n
n
p
CitacióGonzalez, M.; Mazzieri, L. "Singularities for a fully non-linear elliptic equation in conformal geometry". 2013.
Forma part[prepr201311GonM]
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